Axes Intercepts

The intersection points of a line with the axes can be found visually, but this might not be accurate. The exact coordinates can be found algebraically. Note that for all points on the y-axis x=0, similarly all points on the x-axis y=0: convince yourself this true; use the sliders to move the points on the axes:

Intersect with y-axis

We set x=0 and calculate y:

Intersect with x-axis

We set y=0 and calculate x:

Exercise: Calculate the axis intercepts

For the straight line:

calculate the x-intercept and y-intercept coordinates algebraically, and show your working out on paper.

Enter the y-intercept coordinate:

Enter the x-intercept coordinate:

The solution

set x=0

The solution

set y=0

Summary

(i) We set x=0 to find the y intercept. Hence for the line y=mx+c, (c,0) is the y-intercept coordinate.

(ii) We set y=0 to find the x intercept and solve for y; so for the line y=mx+c, (0,-c/m) is the x-intercept coordinate.